MILAN -- Marco Tronchetti Provera has passed the first test as the new owner of Telecom Italia SpA -- lifting the share price -- but in a company that has gobbled up one chairman after another, he has a very long way to go before declaring victory.

Since Mr. Tronchetti Provera took control of Telecom Italia in late July, he has found himself squarely in the hot seat. Shareholders, peeved that Mr. Tronchetti Provera and his partners took over Telecom Italia without paying a premium to minority investors, sent the group's...